510 Mathematik
Refine
Year of publication
- 2024 (4)
- 2023 (10)
- 2022 (45)
- 2021 (43)
- 2020 (80)
- 2019 (59)
- 2018 (47)
- 2017 (52)
- 2016 (24)
- 2015 (32)
- 2014 (18)
- 2013 (24)
- 2012 (30)
- 2011 (6)
- 2010 (17)
- 2009 (13)
- 2008 (17)
- 2007 (13)
- 2006 (34)
- 2005 (32)
- 2004 (35)
- 2003 (22)
- 2002 (28)
- 2001 (30)
- 2000 (25)
- 1999 (27)
- 1998 (23)
- 1997 (17)
- 1995 (2)
- 1994 (4)
- 1992 (1)
- 1991 (1)
- 1990 (1)
- 1980 (1)
Document Type
- Preprint (373)
- Article (274)
- Doctoral Thesis (77)
- Postprint (45)
- Monograph/Edited Volume (13)
- Other (10)
- Master's Thesis (7)
- Conference Proceeding (6)
- Part of a Book (5)
- Review (3)
Language
- English (767)
- German (46)
- French (3)
- Multiple languages (1)
Keywords
- random point processes (18)
- statistical mechanics (18)
- stochastic analysis (18)
- index (14)
- boundary value problems (12)
- Fredholm property (10)
- regularization (10)
- cluster expansion (9)
- elliptic operators (9)
- Bayesian inference (8)
Institute
- Institut für Mathematik (751)
- Institut für Physik und Astronomie (15)
- Extern (14)
- Mathematisch-Naturwissenschaftliche Fakultät (14)
- Hasso-Plattner-Institut für Digital Engineering gGmbH (7)
- Institut für Biochemie und Biologie (6)
- Institut für Informatik und Computational Science (5)
- Department Psychologie (4)
- Hasso-Plattner-Institut für Digital Engineering GmbH (4)
- Department Grundschulpädagogik (3)
Ergodicity of PCA
(2004)
For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.